Influence of water clustering on the dynamics of hydration water at the surface of a lysozyme

Abstract

Dynamics of hydration water at the surface of a lysozyme molecule is studied by computer simulations at various hydration levels in relation with water clustering and percolation transition. Increase of the translational mobility of water molecules at the surface of a rigid lysozyme molecule upon hydration is governed by the water-water interactions. Lysozyme dynamics strongly affect translational motions of water and this dynamic coupling is maximal at hydration levels, corresponding to the formation of a spanning water network. Anomalous diffusion of hydration water does not depend on hydration level up to monolayer coverage and reflects spatial disorder. Rotational dynamics of water molecules show stretched exponential decay at low hydrations. With increasing hydration, we observe appearance of weakly bound water molecules with bulklike rotational dynamics, whose fraction achieves 20-25% at the percolation threshold.

FIGURE 1

Size distribution P(S_max) of the largest water cluster at the surface of a flexible lysozyme molecule at various hydration levels: N_w = 200, 300, 350, 375, 400, 450, 500, and 600. The distribution for N_w = 375, which is the closest to the midpoint of the percolation transition, is shown by the thick line. The vertical dashed line indicates which approximately separates spanning and nonspanning largest clusters.

FIGURE 2

Spanning probability R (upper panel), width ΔS_max of the size distribution of the largest cluster (middle panel), fraction P* of water molecules in the largest cluster, and the normalized average size of water clusters (lower panel) at the surfaces of rigid and flexible lysozyme molecules at various hydration levels. The dashed line in the upper panel represents the fit of R for the flexible lysozyme to the sigmoid function with the inflection point at N_w ≈ 380 indicated by the vertical dotted line. True percolation threshold of water at the surface of the flexible lysozyme is shown by the vertical solid line.

FIGURE 3

Total mean-square displacements 〈r²〉 of water molecules at the surfaces of the flexible and rigid lysozyme molecules at various hydrations N_w shown in legend.

FIGURE 4

Time dependencies of the MSDs 〈r²〉/3, 〈(xy)²〉/2, and 〈z²〉 of water molecules at the surface of a flexible lysozyme molecule at N_w = 500. Solid and dashed lines show the time dependence ∼t^0.40 and ∼t^0.775, respectively.

FIGURE 5

Time dependence of MSD 〈r²〉 of water molecules at surfaces of the flexible and rigid lysozyme molecules in double logarithmic scale (solid lines). Hydration increases from the bottom to the top. The power laws corresponding to the anomalous diffusion (Eq. 2) with different values of α are shown by dashed lines.

FIGURE 6

Time dependence of total MSD 〈r²〉 of water molecules at surfaces of the flexible and rigid lysozyme molecules in double logarithmic scale. The fits to Eqs. 2 and 3 are shown by dashed and solid lines, respectively.

FIGURE 7

Total MSD 〈r²〉 of water molecules at the surface of a flexible lysozyme molecule at t = 10 ps (left upper panel) and its derivative with respect to N_w (left lower panel). Diffusion coefficients D_eff and of water molecules at the surface of a flexible lysozyme molecule (right upper panel) and their derivatives with respect to N_w (right lower panel). Polynomial fits are shown by the dashed lines.

FIGURE 8

Normalized inverse time t(200)/t(N_w), corresponding to the total MSD 〈r²〉 = 0.1 nm² and 〈r²〉 = 1.0 nm² of water molecules at the surface of the flexible and rigid lysozyme molecules as function of the normalized average cluster size Linear dependence is shown by dashed lines in the left panel.

FIGURE 9

Normalized inverse time t(200)/t(N_w), corresponding to the total MSD 〈r²〉 = 1.0 nm² of water molecules at the surface of the flexible and rigid lysozyme molecules as function of the hydration level (upper panel) and of the average number n_H of H-bonded neighbors (lower panel). Linear dependence is shown by dashed line in the lower panel.

FIGURE 10

Total MSD 〈r²〉 at t = 10 ps (upper panel) and inverse time t⁻¹, corresponding to the total MSD 〈r²〉 = 0.1 nm² (lower panel) of water molecules at the surface of a flexible lysozyme molecule as functions of the average number n_H of H-bonded neighbors. Linear fits are shown by dashed lines.

FIGURE 11

The difference Δt⁻¹ between the inverse times, corresponding to the total MSD 〈r²〉 = 0.1 nm² and 〈r²〉 = 1.0 nm² of water molecules at the surfaces of flexible and rigid lysozyme molecules.

FIGURE 12

First-rank dipole-dipole autocorrelation function Γ₁ of water at the surface of a flexible lysozyme at various hydrations N_w. The fits of stretched exponential Eq. 7 to Γ₁ for the lowest and highest hydrations studied are shown by dashed lines. The fits of the data to the two-term Eq. 8 are shown by solid lines.

FIGURE 13

Relaxation times τ₁ and τ₂ found from the fits of Eq. 8 to the first-rank and second rank dipole-dipole autocorrelation functions Γ₁ and Γ₂ of water at the surface of flexible and rigid lysozyme molecules at various hydrations N_w.

FIGURE 14

Amplitude a of the Debye term in Eq. 8, when it is fitted to the first-rank (circles) and second-rank (triangles) dipole-dipole autocorrelation functions Γ₁ and Γ₂ of water at the surface of flexible and rigid lysozymes at various hydrations N_w. Water percolation threshold is shown by the vertical dotted line.

FIGURE 15

(Left panel) Dielectric increment Δε calculated with Eq. 10, taking into account strongly and weakly bound water and excluding the irrotationally bound water (solid line). Experimental data from Bone and Pethig (45) corrected on lysozyme contribution at zero hydration (solid circles). The slope, corresponding to Kirkwood factor g = 2.9, is shown by dashed line. The percolation threshold of water (17) is shown by dotted line. (Right panel) Contribution to Δε from weakly bound water molecules calculated with Eq. 10 (open circles) and experimental data at ν = 25 GHz from Harvey and Hoekstra (44) corrected on lysozyme contribution at zero hydration (solid circles). Appearance of weakly bound water molecules upon hydration is indicated by star.

FIGURE 16

Average number of water-water hydrogen bonds at the surface of a flexible lysozyme molecule and in the rigid lysozyme powder shown as functions of N_w and h.